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Critical exponent of infinite balanced words via the Pell number system

Formal Languages and Automata Theory 2019-11-15 v3 Discrete Mathematics Combinatorics

Abstract

In a recent paper of Rampersad et al., the authors conjectured that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is 3/23/2. We prove this result, using a formulation of first-order logic, the Pell number system, and a machine computation based on finite-state automata.

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Cite

@article{arxiv.1902.00503,
  title  = {Critical exponent of infinite balanced words via the Pell number system},
  author = {Aseem Raj Baranwal and Jeffrey Shallit},
  journal= {arXiv preprint arXiv:1902.00503},
  year   = {2019}
}

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14 pages